Find equivalent fractions to compare. Then, write \( >,< \), or \( = \). \( \frac{3}{5} ? \frac{5}{10} \) \( \frac{3}{5} \frac{5}{10} \)
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The Deep Dive
To compare the fractions \( \frac{3}{5} \) and \( \frac{5}{10} \), we can convert \( \frac{5}{10} \) into an equivalent fraction with the same denominator as \( \frac{3}{5} \). Since \( \frac{5}{10} \) simplifies to \( \frac{1}{2} \), we can rewrite it as \( \frac{3}{5} \) with a common denominator. Next, we multiply both the numerator and denominator of \( \frac{3}{5} \) by 2: \[ \frac{3 \times 2}{5 \times 2} = \frac{6}{10} \] Now we can compare \( \frac{6}{10} \) and \( \frac{5}{10} \). Clearly, \( \frac{6}{10} > \frac{5}{10} \). Thus, we have: \[ \frac{3}{5} > \frac{5}{10} \]
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